A customer orders a round of coffee for her friends. If she orders two 12-ounce cups and one 16-ounce cup, she will owe the coffee shop $10.75. If she orders one 12-ounce cup and two 16-ounce cups, she will owe the coffee shop $11.30. What is the cost for a 16-ounce cup of coffee? A.$3.29 B.$4.25 C.$3.40 D.$3.95

D.$3.95

Step-by-step explanation:

Let us represent

12-ounce cup = x

16-ounce cup = y

A customer orders a round of coffee for her friends.

If she orders two 12-ounce cups and one 16-ounce cup, she will owe the coffee shop $10.75.

Hence:

2x + y = 10.75Equation 1

y = 10.75 - 2x

If she orders one 12-ounce cup and two 16-ounce cups, she will owe the coffee shop $11.30.

Hence:

x + 2y = 11.30Equation 2

We substitute 10.75 -2x for y in Equation 2

x + 2(10.75 - 2x) = 11.30

x + 21.50 - 4x = 11.30

Collect like terms

x - 4x = 11.30 - 21.50

-3x = -10.20

x = -10.20/-3

x = $3.40

Solving for y

y = 10.75 - 2x

y = 10.75 - 2($3.40)

y = 10.75 - 6.8

y = $3.95

Therefore , 16-ounce cup is represented by y, the cost for a 16-ounce cup of coffee is $3.95

Option D is correct